Question

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a newspaper article, the mean of the x distribution is about $34 and the estimated standard deviation is about $7. A button hyperlink to the SALT program that reads: Use SALT. (a) Consider a random sample of n = 80 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying

Answer 1

Kindly check explanation

Explanation:

Given the following :

Population mean (Mp) = 34

Population standard deviation (sd) = $7

Number of customers (n) = 80 customers

According to the central limit theorem:

If the number of samples is large (usually ≥ 30), then the distribution will be normal and mean of sample will be the same as the mean of population.

Population mean(Mp) = sample mean(Ms)

Mp= Ms

$34 = $34

Sample standard deviation = standard error

Standard Error(SE) = (population standard deviation / √n)

SE = 7 / √80

SE = 7 / 8.9442719

SE = 0.7826237 = $0.78

Hence, sample distribution is Normally distributed with a mean of $34 and standard deviation of $0.78